http://www.globalfirepower.com/navy-ships.asp
Maybe in firepower but not in numbers. According to the GFP China and yes, North Korea, have "larger" navies. But it's China and North Korea so they are probably lying or just have a bunch of pontoon boats.
I have to say that is probably not an accurate source. The DPRK is given a strength rating of 967, while maintaining no CVs, no DDs, only 3 FF/FFGs, 2 corvettes, 70 subs and 211 coastal patrol craft; whereas the US is given 415 strength rating with 19 CVs, 6 frigates, 62 DDs, 75 subs and 13 coastal defense craft. China is given the second most at 714, with only 1 CV, 48 FF/FFGs, 32 DDs, 68 subs, 26 corvettes, and 138 coastal patrol craft.
I don't know who put together that site, but their estimations are completely off. Firstly, because the destroyers count is off by 1 (Zumwalt), they don't account for 22 CGs, and they count the LCS as a frigate (which is not, really, more of an oversized coastal patrol craft).
Anyways, I doubt that anyone is challenging the point that the US had the largest fleet in World War II.
ALSO, as to the carrier killer missiles... those aren't 100% either. First, you have to find the carrier; then you have to hit the carrier; then you have to actually hit it hard enough or often enough to sink it.